A DSMC Model on Droplet Clusters to Explore the Limiting Factors of Modified Surfaces Promoting Enhanced Dropwise Condensation

Abstract

Condensation is a physical process that occurs when a vapor is cooled and/or compressed to its saturation limit. Condensation becomes important in a variety of engineering applications such as in heat exchangers used for distillation purposes. In such instances, higher condensation efficiencies are desirable. Research to improve condensation has focused on dropwise condensation as it has been shown that it can be significantly more efficient than filmwise condensation. Recent investigations of dropwise condensation on nanostructured surfaces suggest that enhanced dropwise condensation can be attained as the average droplet sizes are reduced for clusters growing through dropwise condensation. This, in turn, significantly enhances the heat transfer coefficients of dropwise condensation. This paper summarizes a computational model developed to explore the mechanisms leading to this enhanced dropwise condensation. A Direct Simulation Monte Carlo (DSMC) approach is used here to investigate the mechanisms and limitations of enhanced dropwise condensation for these surfaces aiming to reduce the average droplet sizes of condensation. For computational purposes, several idealizations are assumed by the model, which include: (1) The condensation droplet clusters are assumed to have uniform size, corresponding to an average droplet size observed in actual dropwise condensation scenarios; (2) Due to the assumed uniform droplet distribution, symmetry can be observed from the droplet cluster, so a small but symmetrical cross section of the droplet distribution is used for the computational domain; and (3) Supersaturated steam condensing on a cold wall is assumed for most of the simulations. The mechanisms at play that are deliberately explored are: (1) The effects of surface wettability by using a model that considers droplet conduction variations with varying contact angle; (2) The changes of interfacial resistance with droplet curvature by introducing a surface tension model based on the Tolman length; and (3) The dynamic interactions between neighboring droplets by choosing our computational domain to be a symmetrical cross section that encompasses surrounding droplets in an appropriate fashion. The ambient conditions that were investigated were: (1) Varying atmospheric pressure; (2) Varying amounts of wall subcooling for the droplets; (3) Varying accommodation for water molecules condensing on the droplet; and (4) The introduction of air into the assumed supersaturated steam condensing on the cold wall. To investigate the overall and combined effects of the aforementioned mechanisms on enhanced dropwise condensation through reduced droplet sizes, the simulations were run for droplets with radii between 1 micrometer down to 5 nanometers. The model predictions indicate that the larger droplet transport trend of increasing heat transfer with decreasing droplet sizes breaks down as droplet sizes become smaller due to more prominence of the mechanisms hindering condensation for the reduced droplet sizes. As the model breaks down, a peak heat transfer is reached, and heat transfer is further reduced as the average droplet sizes continue to decrease. The predictions of this particular DSMC model are compared to previous work investigating similar effects. The implications of our observations and potential impact to current and future research in the area is discussed in detail.

On Localized Vapor Pressure Gradients Governing Condensation and Frost Phenomena

“…In an all-liquid condensing system, these dry zones are driven solely by the difference in supersaturation degree (SSD) between droplets of disparate sizes. There exist some rigorous computational studies that have solved for the heat transfer coefficients and droplet growth by numerically solving the transport equations. , Here, we show by simple scaling arguments how we can estimate the dry zone length between droplets over a wide parameter space. Consider a mother droplet exhibiting a radius of curvature r m = 10 μm and a temperature T d at its liquid–vapor interface.…”

“…However, the model is based on simple scaling arguments and more importantly on the continuum limit where fluxes are governed by eqs and . A computational model in this regard , can help shed more light on the noncontinuum transport effects on dry zones in the very early stages of nucleation when r ∼ 1–10 nm.…”

“…Homogeneous nucleation has been addressed in considerable depth in the fields of cloud physics and atmospheric sciences. , For this reason and also because the phenomena of dry zones, ice bridging, and frost halos are generally intrinsic to substrates, we limit ourselves here to the case of heterogeneous nucleation. Note that in the present discussion we have not considered the noncontinuum transport effects that have been studied in previous works, − which if considered would not change the formulation but use a different value of surface tension. We will first consider the case of new water/ice embryos nucleating on a dry portion of the substrate.…”

“…It can be seen that the supersaturation is quite significant for nanometric droplets (for example, SSD > 1 when r ∼ 1 nm) but becomes insignificant (<0.1% supersaturation) for micrometric droplets whose vapor pressure can be approximated as saturated. Note that in order to obtain better estimates of SSD, curvature-induced changes in surface tension − should be considered when the droplet curvature becomes comparable to the thickness of the liquid–vapor interface.…”